Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Pair-breaking quantum phase transition in superconducting nanowires

An Author Correction to this article was published on 18 July 2018

This article has been updated


Quantum phase transitions (QPT) between distinct ground states of matter are widespread phenomena1,2,3,4,5, yet there are only a few experimentally accessible systems6,7 where the microscopic mechanism of the transition can be tested and understood. These cases are unique and form the experimentally established foundation for our understanding of quantum critical phenomena. Here we report that a magnetic-field-driven QPT in superconducting nanowires—a prototypical one-dimensional system (d=1)—can be fully explained by the critical theory8,9 of pair-breaking transitions characterized by a correlation length exponent v≈1 and dynamic critical exponent z≈2. We find that in the quantum critical regime, the electrical conductivity is in agreement with a theoretically predicted scaling function and, moreover, that the theory quantitatively describes the dependence of conductivity on the critical temperature, field magnitude and orientation, nanowire cross-sectional area, and microscopic parameters of the nanowire material. At the critical field, the conductivity follows a T(d–2)/z dependence predicted by phenomenological scaling theories10,11 and more recently obtained within a holographic framework12. Our work uncovers the microscopic processes governing the transition: the pair-breaking effect of the magnetic field on interacting Cooper pairs overdamped by their coupling to electronic degrees of freedom. It also reveals the universal character of continuous quantum phase transitions.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Schematic phase diagram for the pair-breaking superconductor to metal quantum phase transition in nanowires.
Fig. 2: Superconductor–metal transition in nanowires.
Fig. 3: Finite-size scaling analysis.
Fig. 4: Quantitative test of the pair-breaking QPT theory.

Change history

  • 18 July 2018

    In the version of this Letter originally published, one of the authors’ first names was incorrectly spelled Fédéric; it should have read Frédéric. This has now been corrected.


  1. 1.

    Steppke, A. et al. Ferromagnetic quantum critical point in the heavy-fermion metal YbNi4(P1−xAsx)2. Science 339, 933–936 (2013).

    ADS  Article  Google Scholar 

  2. 2.

    Marković, N., Christiansen, C. & Goldman, A. M. Thickness–magnetic field phase diagram at the superconductor–insulator transition in 2d. Phys. Rev. Lett. 81, 5217–5220 (1998).

    ADS  Article  Google Scholar 

  3. 3.

    Zhang, X., Hung, C.-L., Tung, S.-K. & Chin, C. Observation of quantum criticality with ultracold atoms in optical lattices. Science 335, 1070–1072 (2012).

    ADS  Article  Google Scholar 

  4. 4.

    Cejnar, P., Jolie, J. & Casten, R. F. Quantum phase transitions in the shape of atomic nuclei. Rev. Mod. Phys. 82, 2155–2212 (2010).

    ADS  Article  Google Scholar 

  5. 5.

    Alford, M. G., Schmitt, A., Rajagopal, K. & Schäfer, T. Color superconductivity in dense quark matter. Rev. Mod. Phys. 80, 1455–1516 (2008).

    ADS  Article  Google Scholar 

  6. 6.

    Lake, B., Tennant, D. A., Frost, C. D. & Nagler, S. E. Quantum criticality and universality scaling of a quantum ferromagnet. Nat. Mater. 4, 329–334 (2005).

    ADS  Article  Google Scholar 

  7. 7.

    Potok, R. M., Rau, I. G., Shtrikman, H., Oreg, Y. & Goldhaber-Gordon, D. Observation of the two-channel Kondo effect. Nature 446, 167–171 (2007).

    ADS  Article  Google Scholar 

  8. 8.

    Del Maestro, A., Rosenow, B., Shah, N., & Sachdev, S. Universal thermal and electrical transport near the superconductor–metal quantum phase transition in nanowires. Phys. Rev. B 77, 180501 (R) (2008).

    Article  Google Scholar 

  9. 9.

    Del Maestro, A., Rosenow, B. & Sachdev, S. Theory of the pairbreaking superconductor–metal transition in nanowires. Ann. Phys. 324, 523–583 (2009).

    ADS  Article  MATH  Google Scholar 

  10. 10.

    Fisher, M. P. A., Weichmann, P. B., Grinstein, G. & Fisher, D. C. Boson localization and the superfluid–insulator transition. Phys. Rev. B 40, 546–570 (1989).

    ADS  Article  Google Scholar 

  11. 11.

    Damle, K. & Sachdev, S. Nonzero-temperature transport near quantum critical points. Phys. Rev. B 56, 8714–8733 (1997).

    ADS  Article  Google Scholar 

  12. 12.

    Hartnoll, S.A., Lucas, A. & Sachdev, S. Holographic Quantum Matter (MIT Press, Cambridge, MA, 2018).

  13. 13.

    Bollinger, A. T. et al. Superconductor–insulator transition in La2−xSrxCuO4 at the pair quantum resistance. Nature 472, 458–460 (2011).

    ADS  Article  Google Scholar 

  14. 14.

    Ovadia, M., Kalok, D., Sacépé, B. & Shahar, D. Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition. Nat. Phys. 9, 415–418 (2013).

    Article  Google Scholar 

  15. 15.

    Stewart, M. D., Yin, A., Xu, J. M., & Valles, J. M. Superconducting pair correlations in an amorphous insulating nanohoneycomb film. Science 318, 1273–1275 (2007).

    ADS  Article  Google Scholar 

  16. 16.

    Jin, K., Butch, N. P., Kirshenbaum, K., Paglione, J. & Greene, R. L. Link between spin fluctuations and electron pairing in copper oxide superconductors. Nature 476, 73–75 (2011).

    Article  Google Scholar 

  17. 17.

    Yazdani, A. & Kapitulnik, A. Superconductor–insulating transition in two-dimensional a-MoGe thin films. Phys. Rev. Lett. 74, 3037–3040 (1995).

    ADS  Article  Google Scholar 

  18. 18.

    Bezryadin, A. Superconductivity in Nanowires (Wiley, Weinheim, 2013).

    Google Scholar 

  19. 19.

    Arutyunov, K. Yu, Golubev, D. S. & Zaikin, A. D. Superconductivity in one dimension. Phys. Rep. 464, 1–70 (2008).

    ADS  Article  Google Scholar 

  20. 20.

    Sahu, M. et al. Individual topological tunnelling events of a quantum field probed through their macroscopic consequences. Nat. Phys. 5, 503–508 (2009).

    Article  Google Scholar 

  21. 21.

    Li, P. et al. Switching currents limited by single phase slips in one-dimensional superconducting Al nanowires. Phys. Rev. Lett. 107, 137044 (2011).

    ADS  Google Scholar 

  22. 22.

    Kim, H., Jamali, S. & Rogachev, A. Superconductor–insulator transition in long MoGe nanowires. Phys. Rev. Lett. 109, 027002 (2012).

    ADS  Article  Google Scholar 

  23. 23.

    Makise, K., Terai, H., Tominari, Y., Tanaka, S. & Shinozaki, B. Duality picture of superconductor–insulator transition on superconducting nanowire. Sci. Rep. 6, 27001 (2016).

    ADS  Article  Google Scholar 

  24. 24.

    Ning, W. et al. Superconductor–insulator transition in quasi-one-dimensional single-crystal Nb2PdS4 nanowires. Nano Lett. 15, 869–875 (2015).

    ADS  Article  Google Scholar 

  25. 25.

    Shah, N. & Lopatin, A. Microscopic analysis of the superconducting quantum critical point: Finite-temperature crossovers in transport near a pair-breaking quantum phase transition. Phys. Rev. B 76, 094511 (2007).

    ADS  Article  Google Scholar 

  26. 26.

    Kim, H. & Rogachev, A. Zero-bias anomaly in homogeneously disordered MoGe nanowires undergoing superconductor–insulator transition. Phys. Rev. B 94, 254436 (2016).

    Google Scholar 

  27. 27.

    Kuo, W. & Chen, C. H. Scaling analysis of magnetic-field-tuned phase transition in one-dimensional Josephson junction array. Phys. Rev. Lett. 87, 186804 (2001).

    ADS  Article  Google Scholar 

  28. 28.

    Mason, N. & Kapitulnik, A. Dissipation effect on the superconductor–insulator transition in 2d superconductors. Phys. Rev. Lett. 82, 5341–5344 (1999).

    ADS  Article  Google Scholar 

  29. 29.

    Galitski, V. Nonperturbative microscopic theory of superconducting fluctuations near a quantum critical point. Phys. Rev. Lett. 100, 127001 (2008).

    ADS  Article  Google Scholar 

  30. 30.

    Hoyos, J. A., Kotabage, C. & Voita, T. Effect of dissipation on a quantum critical point with disorder. Phys. Rev. Lett. 99, 230601 (2007).

    ADS  Article  Google Scholar 

  31. 31.

    Rogachev, A., Bollinger, A. T. & Bezryadin, A. Influence of high magnetic fields on the superconducting transition of one-dimensional Nb and MoGe nanowires. Phys. Rev. Lett. 94, 017004 (2005).

    ADS  Article  Google Scholar 

  32. 32.

    Kim, H. et al. Effect of magnetic Gd impurities on the superconducting state of amorphous Mo-Ge thin films with different thickness and morphology. Phys. Rev. B 86, 024518 (2012).

    ADS  Article  Google Scholar 

  33. 33.

    I. F. Herbut, I. F. Zero-temperature d-wave superconducting phase transition. Phys. Rev. Lett. 85, 1532–1535 (2000).

    ADS  Article  Google Scholar 

  34. 34.

    Del Maestro, A., Rosenow, B., Müller, M. & Sachdev, S. Infinite randomness fixed point of the superconductor–metal quantum phase transition. Phys. Rev. Lett. 101, 035701 (2008).

    ADS  Article  Google Scholar 

  35. 35.

    Thouless, D. J. Maximum metallic resistance in thin wires. Phys. Rev. Lett. 39, 1167–1169 (1977).

    ADS  Article  Google Scholar 

  36. 36.

    Lopatin, A. V., Shah, N. & Vinokur, V. M. Fluctuation conductivity of thin films and nanowires near a parallel-field-tuned superconducting quantum phase transition. Phys. Rev. Lett. 94, 037003 (2005).

    ADS  Article  Google Scholar 

  37. 37.

    Tinkham, M. Introduction to superconductivity 2nd edn (Dover, Mineola, 1996).

    Google Scholar 

  38. 38.

    Tucker, J. R. & Halperin, B. I. Onset of superconductivity in one-dimensional systems. Phys. Rev. B 3, 3768–3781 (1971).

    ADS  Article  Google Scholar 

  39. 39.

    Konig, E. J. et al. Berezinskii–Kosterlitz–Thouless transition in homogeneously disordered superconducting films. Phys. Rev. B 92, 214503 (2015).

    ADS  Article  Google Scholar 

Download references


The authors thank N. Shah, B. Rosenow, S. Sachdev and O. Starykh for valuable comments. Nanowire fabrication was carried out at the University of Utah Microfab and USTAR facilities. A.R. acknowledges Université Grenoble Alpes and Institute Néel, where measurements were performed, for hospitality. This research was supported in part by the National Science Foundation under award numbers DMR-1611421 (A.R.) and DMR-1553991 (A.D.) and by the ERC Grant QUEST number 637815 (B.S.). A.D. performed a portion of this work at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611.

Author information




H.K. fabricated nanowires, A.R., B.S. and F.G. carried out measurements, A.R., B.S. and A.D. carried out data analysis and wrote the manuscript, A.R. conceived and coordinated the project.

Corresponding author

Correspondence to Andrey Rogachev.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

2 Tables, 1 Figure, 11 References

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kim, H., Gay, F., Del Maestro, A. et al. Pair-breaking quantum phase transition in superconducting nanowires. Nature Phys 14, 912–917 (2018).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing